Cuts and connectivity in graphs and hypergraphs

In this thesis, we consider cut and connectivity problems on graphs, digraphs, hypergraphs and hedgegraphs. The main results are the following: - We introduce a faster algorithm for finding the reduced graph in element-connectivity computations. We also show its application to node separation. - We present several results on hypergraph cuts, including (a) a near linear time algorithm for finding a (2+epsilon)-approximate min-cut, (b) an algorithm to find a representation of all min-cuts in the same time as finding a single min-cut, (c) a sparse subgraph that preserves connectivity for hypergraphs and (d) a near linear-time hypergraph cut sparsifier. - We design the first randomized polynomial time algorithm for the hypergraph k-cut problem whose complexity has been open for over 20 years. The algorithm generalizes to hedgegraphs with constant span. - We address the complexity gap between global vs. fixed-terminal cuts problems in digraphs by presenting a 2-1/448 approximation algorithm for the global bicut problem.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Xu, Chao

Contributors dc:contributor

• Chandrasekaran, Karthekeyan
• Chekuri, Chandra
• Erickson, Jeff
• Király, Tamás

• hypergraph
• cuts

Statement dc:rights

• Copyright 2018 Chao Xu

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101009

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101009